Data Structures/Tradeoffs

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Data Structures
Introduction - Asymptotic Notation - Arrays - List Structures & Iterators
Stacks & Queues - Trees - Min & Max Heaps - Graphs
Hash Tables - Sets - Tradeoffs

It is important to fully understand the problem you need to solve before choosing a data structure because each structure is optimized for a particular job. Hash tables, for example, favor fast lookup times over memory usage while arrays are compact and inflexible. Other structures, such as stacks, are optimized to enforce rigid rules on how data is added, removed and accessed throughout the program execution. A good understanding of data structures is fundamental because it gives us the tools for thinking about a program's behavior in a structured way.

 [TODO:]
 Use asymptotic behaviour to decide, most importantly seeing how the
 structure will be used: an infrequent operation does not need to be
 fast if it means everything else will be much faster


 [TODO:]
 Can use a table like this one to compare the asymptotic behaviour of every
 structure for every operation on it.
Sequences (aka lists):
Array Dynamic Array Array Deque Singly Linked List Double Linked List
Push (Front) - O(n) O(1) O(1) O(1)
Pop (Front) - O(n) O(1) O(1) O(1)
Push (Back) - O(1) O(1) O(n), maybe O(1)* O(1)
Pop (Back) - O(1) O(1) O(n) O(1)
Insert before (given iterator) - O(n) O(n) O(n) O(1)
Delete (given iterator) O(n) O(n) O(n) O(1)
Insert after (given iterator) O(n) O(n) O(1) O(1)
Delete after (given iterator) - O(n) O(n) O(1) O(1)
Get nth element (random access) O(1) O(1) O(1) O(n) O(n)
Good for implementing stacks no yes (back is top) yes yes (front is top) yes
Good for implementing queues no no yes maybe* yes
C++ STL std::array std::vector std::deque std::forward_list std::list
Java Collections java.util.Array java.util.ArrayList java.util.ArrayDeque - java.util.LinkedList
* singly-linked lists can push to the back in O(1) with the modification that you keep a pointer to the last node


Associative containers (sets, associative arrays)
Sorted Array Sorted Linked List Self-balancing Binary Search Tree Hash Table
Find key O(log n) O(n) O(log n) O(1) average O(n) worst
Insert element O(n) O(n) O(log n) O(1) average O(n) worst
Erase key O(n) O(n) O(log n) O(1) average O(n) worst
Erase element (given iterator) O(n) O(1) O(1) O(1)
Can traverse in sorted order? yes yes yes no
Needs comparison function comparison function comparison function hash function
C++ STL - - std::set
std::map
std::multiset

std::multimap

std::unordered_set
std::unordered_map
std::unordered_multiset

std::unordered_multimap

Java Collections - - java.util.TreeSet

java.util.TreeMap

java.util.HashSet

java.util.HashMap

  • Please correct any errors
Various Types of Trees
Binary Search AVL Tree Binary Heap (min) Binomial Queue (min)
Insert element O(log n) O(log n) O(log n) O(1) (on average)
Erase element O(log n) O(log n) unavailable unavailable
Delete min element O(log n) O(log n) O(log n) O(log n)
Find min element O(log n) O(log n) O(1) O(log n) (can be O(1) if ptr to smallest)
Increase key unavailable unavailable O(log n) O(log n)
Decrease key unavailable unavailable O(log n) O(log n)
Find O(log n) O(log n) unavailable unavailable
Delete element O(log n) O(log n) unavailable unavailable
Create O(1) O(1) O(1) O(1)
find kth smallest O(log n) O(log n) O((k-1)*log n) O(k*log n)
Hash table
Hash table (hash map)
Set Value Ω(1), O(n)
Get Value Ω(1), O(n)
Remove Ω(1), O(n)
 [TODO:]
 Can also add a table that specifies the best structure for some specific need
 e.g. For queues, double linked. For stacks, single linked. For sets, hash tables. etc...
 [TODO:]
 Could also contain table with space complexity information (there is a significative cost
 in using hashtables or lists implemented via arrays, for example).


Data Structures
Introduction - Asymptotic Notation - Arrays - List Structures & Iterators
Stacks & Queues - Trees - Min & Max Heaps - Graphs
Hash Tables - Sets - Tradeoffs